Petri Nets and Matrix Graph Grammars: Reachability

This paper contributes in two directions. First, several concepts of our matrix approach to graph transformation [1,2] such as coherence and minimal initial digraph are applied to Petri nets, especially to reachability criteria. Second, the state equation and related algebraic Petri net techniques for reachability are generalized using tensor algebra to cover a wider class of rewriting systems. 1 Applying Matrix Graph Grammar Techniques to Petri Nets Our approach to graph transformation works with simple digraphs, which can be represented as a boolean matrix for edges, and a boolean vector for nodes. A production can be represented by two boolean matrices and two vectors p = LE , RE ; LN , RN , where E stands for edges and N for nodes. The actions that can be performed by a production are deletion (e) and addition (r), having two associated matrices each one eE , rE ; eN , rN . The output of a production p is defined by RE = rE eE LE and similar for nodes. We call compatibility to the ...

• Type: Journal
• Year: 2006
• Where: ECEASST
• Authors: Juan de Lara, Pedro Pablo Pérez Velasco
• Keywords: ECEASST 2006, Minimal Initial Digraph, Petri Nets, Simple Digraph